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Assume that you have a way to easily solve the RP for a given $n$. Now I give you $G$ and $P$ on the curve (of size $q$), and I want you to find $x$ such that $P = xG$. What you do is the following: you generate random integers $r_1, r_2, \cdots, r_n \mod q$, and compute $Q_i = r_iG$ for all $i$ from $1$ to $n$. Then you solve RP for P relatively to those $Q_i$, yielding the $a_i$. You then get $x = a_1r_1 + a_2r_2 + \cdots + a_nr_n \mod q$.